The Paradigm of Mathematics in Teaching Learning

Mathematics is a branch of knowledge that deals with numbers. Some people think it is a complicated subject to learn. But they can not avoid living with it. Counting, measuring, adding, subtracting, dividing, and multiplying are the kind where we live. Also we often play the puzzling games using mathematics. So mathematics is needed to learn.
There are two kind of Mathematics learning, they are pure mathematics and elementary mathematics. Elementary mathematics is studied by primary students at elementary school and junior high school. Elementary mathematics is given to primary students because they can not accept abstract materials. It must be explained by concrete things so the material is easier to accept. Example of concrete objects are drum, tube, wheel and others things that similar with mathematical object. They are learned by observation.
The abstract material on math will be given to adult people like students in university and students in senior high school. As geometry, algebra, matrices, calculus are beyond mind of people, so it must be given slowly and with right method.
The different abstract and concrete object lays on the characteristic of object. Object in pure mathematics is perfect object that is main object. But in concrete object that just on measurement and shape. It is not mathematical object. To get mathematical object we use abstraction. It means take certain characteristic that we want to learn. And we use idealism. It means put down as the perfect characteristic.
Mathematics is not release from problem solving, proving and building theorem systematically. It is also developed in formal system form. Math in this case is also called pure mathematics. It is learned by student in university. The formal system form is called mathematics axiomatic. But just some particular people absolutely learn mathematics in high grade.
On the other hand, mathematics in primary school always have problem to communicate it. For younger people, math is difficult to understand. So, in school, we need easy to talk math. Moreover, mathematics can be good and easy to learn for younger people. So, mathematics can be adaptable in teaching learning.
Many people in the world learn mathematics, but just some of them know the nature of mathematics. Actually knowing the nature of mathematics is importance. It is part when we learn math. There are four nature of mathematics. They are:
1. Mathematics research for pattern and relationship.
2. Mathematics is problem solving activity.
3. Mathematics is investigation activity.
4. Mathematics is a mean of communication.
There are four items on the nature of student learn math, so student learn math effectively.
1. Student has good motivation and good preparation.
2. Student can learn math in collaboration with others.
3. Student can learn math individually.
4. Student learn math contextually.
From explanation above, we need a manner to teach mathematics. So, that the materials are accepted effectively. By using method of learning math, we can communicate mathematics. There are two streams of teaching method. First is traditional teaching. It is old paradigm. It shows that teacher predominantly on student activity and student initiation. Teacher is very active. So lesson will be abstract and more theoretical. Students as empty vessel, so they are passive, they only listen material. It makes students feel boring. So they think mathematics is very formal and difficult to accept.
Traditional method has applied on school since yore. The teacher explained material and students did worksheet. The teacher-centered approach assumes that all students have similar levels of knowledge in the subject being taught and they absorb new material in a similar pace. The advantages of traditional methods are to make student become responsibilities for teaching in the classroom, to make sure everything they thought were understood by the student. Thus it was a good method, where there was efficient communication between teacher and students. It makes class to be controllable where the teacher would teach on the blackboard, explained, asks students to copy and make sure students paid attention and listen. Besides that, it is building a good characteristic student effectively because students always respect to their teacher.
The traditional is also a way in disciplining students in school. But it make students get traumatizes in school and to be afraid with teacher. Traditional method is easy method where education transforms from teacher to students. It is classical learning; the students do not know what purpose they learn on that day.
The second stream is contemporary method or innovative teaching. This is a new paradigm. Innovative teaching also called constructivist teaching shows that teacher as facilitator. So education can not transform from teacher to students, but education is empowering of students. Teacher is aware that every student has the unique ability. So they are different. And teacher should teach each student with difference way. The student-centered learning approach allows students to work together in small groups and answer a posed question. In this paradigm, students are seeds, where they can grow and bear fruits. So students will be active.
Innovative teaching builds relationship between teacher and students, where each of them will contribute in teaching learning. Teacher is to be their friend. So they can share their problems to the teacher without being afraid. Students can develop their personality suit one’s fancy. It consists on agreement between teachers and student regarding on behave in the classroom to start building a student’s expectation towards independence.
Yuen and Hau stated further that constructivist teaching is guided by the following principles: problems are posed to students that have emerging relevance; concepts are structured from whole to part; student vides are valued and addressed; and student learning is assessed in context. Thus, this method presents students with problems that are authentic and relevant to them and allows them to find their own solutions as they build knowledge.
To develop constructivist teaching, we need technology, especially computer. Computer will help teacher and student when they work and do anything. Teachers can prepare their work and present it to the class by slides show which is an easier way. By slides show, learning in classroom can be interesting. In addition, students get information and knowledge by computer where access with internet. On the other hand computer can disturb teaching when it does not use effectively. For example, with use of computers in school children gets distracted with online games and websites to browse on besides their studies. So teacher should monitoring students when study at school.
Every method has advantages and disadvantages. So, teacher must be aware when he or she teach students especially mathematics. But we must solve how to move old paradigm to new paradigm. Because of new paradigm more appropriate with this time and useful. It will become the manner to get the success teacher in mathematics if we see the nature of mathematics and the nature of student learn effectively. The most importance is using constructivist teaching with less the disadvantages. Teacher must give motivation to the student. So they feel interesting and more explore their ability.

 
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http://smp3lembang.blogspot.com/2011/02/traditional-way-in-teaching-learning.html
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